TORSIONAL OSCILLATIONS OF WIRES. 431 



since it gives the value of a //-unit, which, in each case, makes b take the absolutely 

 constant value A. Its magnitude is given by the relation 



,*■ -(!)". 



If a simple expression such as this, connecting the Unifying Angle with the observed 

 quantities n and b in each experiment, did not exist, we could not regard that angle as 

 a quantity possessing any physical importance whatsoever. Indeed, we could not re- 

 gard it as such unless the quantity A is found by experiment to correspond to some 

 physical constant. 



A glance at figs. 5-12 makes it apparent that, in each series of experiments, 

 the Hues representing the linear relations already discussed, pass with great accuracy 

 through the point corresponding to n — 1, log b = 2 '3. The value b = 200 is therefore 

 of distinct physical importance in all the series. By giving A this value, and eliminat- 

 ing B and /3 from the linear equations, we get 



VA/ , 

 and 



Thus the Inverse and Critical Angles have also simple expressions in terms of b and n. 



The quantity A is an Oscillation Constant which depends essentially upon the 

 material of which the wire is made. Further evidence regarding its constancy will be 

 given immediately. 



Second Series of Experiments. 



In order to obtain further evidence on points already referred to, a second series of 

 experiments, commencing on the date 14.10.97, was made. Between that date and 

 the date 30.7.96, on which the first series was concluded, the wire had not been 

 oscillated except on a few occasions in November 1896, and again in March 1897. 

 The results are given in Table V. 



At the end of the first experiment it was found that 36|- full oscillations took place 

 in 5 minutes when the oscillations were large, while 37 took place in the same time 

 when the oscillations were small. At the end of the experiment dated 15.11.97 (1), 

 38 half oscillations took place in 2\ minutes when the oscillations were small. 



The values of a, n, and b, which are obtained when y is very small, are extremely 

 uncertain ; yet there is no doubt that the value of n is considerably less than unity 

 uuder that condition, and that the value of b is large. 



In the earlier experiments of this series there is evidence that the wire had 

 recovered to a slight extent from the state of fatigue induced in the first series. But 



